5 papers
Moment generating function of the tacnode process
Taiyang Xu
The tacnode process is a universal determinantal point process arising in non-intersecting particle systems and random tiling models. In this paper, we study the generating functio…
On the large-time asymptotics of the defocusing mKdV equation with step-like initial data
Taiyang Xu, Yidan Zhang
We study the Cauchy problem for the defocusing modified Korteweg-de Vries (mKdV) equation with step-like initial data approaching nonzero constants and as $x \to -\inft…
Confluent hypergeometric kernel determinant on multiple large intervals
Taiyang Xu, Lun Zhang, Zhengyang Zhao
The confluent hypergeometric point process represents a universality class which arises in a variety of different but related areas. It particularly describes the local statistics…
Painlevé transcendents in the defocusing mKdV equation with non-zero boundary conditions
Zhaoyu Wang, Taiyang Xu, Engui Fan
We consider the Cauchy problem for the defocusing modified Korteweg-de Vries (mKdV) equation with non-zero boundary conditions \begin{align} &q_t(x,t)-6q^2(x,t)q_{x}(x,t)+q_{xxx}(x…
Soliton resolution and asymptotic stability of -soliton solutions for the defocusing mKdV equation with a non-vanishing background
Zechuan Zhang, Taiyang Xu, Engui Fan
We analytically study the large-time asymptotics of the solution of the defocusing modified Korteweg-de Vries (mKdV) equation under a symmetric non-vanishing background, which supp…